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   VI-TireScrub &gt; <a href="drvsim_motioncueing_tire_scrub_effect_cueing.htm">Tire Scrub Effect</a>&nbsp;&gt;</p>
      <h1 class="p_Heading1" style="page-break-after: avoid;"><span class="f_Heading1">Physical Dependencies and Tuning Parameters</span></h1>

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<p class="p_Normal">The basic principle beyond the Tire Scrub Effect is adding a sinusoidal, zero-average disturbance to the lateral force channels. Based on the input variables that are governing the algorithm, this disturbance signal is instantaneously stretched in amplitude and frequency by means of a chain of multipliers.</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">There are 4 gains acting as multipliers, each of them scaling the zero-average disturbance with respect to the relative dependency:</p>
<p class="p_Normal">&nbsp;</p>
<p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 48px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span> Lateral Margin (linked to the internal TireLimits dependencies previously listed)</p><p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 48px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span> Tire Longitudinal Slip Ratio</p><p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 48px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span> Tire Normal Load</p><p style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 13px; margin: 0px 0px 0px 48px;"><span style="font-size:10pt; font-family: 'Arial Unicode MS','Lucida Sans Unicode','Arial';color:#000000;display:inline-block;width:13px;margin-left:-13px">&#8226;</span> Wheel Omega</p><p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><span style="font-weight: bold;">Baseline case study</span></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">To explain how each variable is affecting the output channels, a Constant Radius Circle maneuver is used as an example. In this maneuver a FWD car is driven to its lateral limit, gradually building up its lateral acceleration, until the Tire Scrub mechanism is activated and the disturbance is added to lateral forces at each corner of the car.</p>
<p class="p_Normal">In the following plots, lateral forces for the four hub carriers are shown: comparison is between the maneuver run without Tire Scrub Effect (red) and with Tire Scrub Effect (blue).</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><img alt="drvsim_scrub_02" width="1664" height="877" style="margin:0;width:1664px;height:877px;border:none" src="drvsim_scrub_02.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">It’s possible to notice that forces for the loaded pair of wheels, external to the corner, are growing undisturbed until the Tire Scrub Effect intervenes.</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><span style="font-weight: bold;">Gain Over Lateral Margin</span></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">This gain is managing the tire scrub activation with respect to the lateral margin computed by internal Vi-TireLimits tool. The multiplier is defined by a semi-gaussian function that can be tuned by means of two parameters, Threshold_M and Smoothness_M, to modify the shape of the gain.</p>
<p class="p_Normal">Threshold_M represents the lateral margin force (measured in Newton): the lower the value, the later the effect is activated in terms of distance between the working point of the tire and its instantaneous limit friction ellipse. In the following pictures, the test case maneuver is run with 2 different threshold forces, highlighting the effect of Threshold_M in isolation.</p>
<p class="p_Normal">&nbsp;</p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Parameter Value</span></p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Analysis Colour</span></p>
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<td style="vertical-align:middle; width:433px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Baseline</span></p>
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<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Threshold_M=2000[N]</p>
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<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Blue</p>
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<td style="vertical-align:middle; width:433px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Mod</span></p>
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<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Threshold_M=1500[N]</p>
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<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Red</p>
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<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal" style="text-align: center;"><img alt="drvsim_scrub_03" width="359" height="318" style="margin:0px auto 0px auto;width:359px;height:318px;border:none" src="drvsim_scrub_03.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><img alt="drvsim_scrub_04" width="1664" height="877" style="margin:0;width:1664px;height:877px;border:none" src="drvsim_scrub_04.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">With the Smoothness_M parameter, it is instead possible to tune the slope of the gain, managing the smoothness of the transition between 0 and 1 gain: the higher the number, the steeper the slope, the harsher the transition. The effect of this parameter in isolation is shown in the following pictures.</p>
<p class="p_Normal">&nbsp;</p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Parameter Value</span></p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Analysis Colour</span></p>
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<td style="vertical-align:middle; width:433px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Baseline</span></p>
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<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Smoothness_M=1</p>
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<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Blue</p>
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<td style="vertical-align:middle; width:433px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Mod</span></p>
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<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Smoothness_M=0.2</p>
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<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Red</p>
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<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal" style="text-align: center;"><img alt="drvsim_scrub_07" width="359" height="318" style="margin:0px auto 0px auto;width:359px;height:318px;border:none" src="drvsim_scrub_07.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><img alt="drvsim_scrub_08" width="1664" height="877" style="margin:0;width:1664px;height:877px;border:none" src="drvsim_scrub_08.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><span style="font-weight: bold;">Gain Over Lognitudinal Slip</span></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">This gain is used to manage the activation of Tire Scrub Effect with respect to the longitudinal slip of the tire, in situations where the tires are worked in combined grip conditions. The physical phenomenon of tire scrub is typically erased when high longitudinal slips are present in combination with low lateral margins, because the tire is pushed towards complete dynamic friction at contact patch. This is particularly true when power is applied on a FWD car while the front tires are already near their lateral friction limits.</p>
<p class="p_Normal">The dependency from longitudinal slip is implemented with a semi-gaussian function, analogous to the gain over lateral margin. The two tuning parameters are Threshold_LS and Smoothness_LS. </p>
<p class="p_Normal">In the following pictures, the test case maneuver is run with two different threshold slips (measured in percentage), highlighting the effect of Threshold_LS in isolation.</p>
<p class="p_Normal">&nbsp;</p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Parameter Value</span></p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Analysis Colour</span></p>
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<td style="vertical-align:middle; width:433px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Baseline</span></p>
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<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Threshold_LS =10[%]</p>
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<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Blue</p>
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<td style="vertical-align:middle; width:433px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Mod</span></p>
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<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Threshold_LS =4[%]</p>
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<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Red</p>
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<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal" style="text-align: center;"><img alt="drvsim_scrub_09" width="359" height="318" style="margin:0px auto 0px auto;width:359px;height:318px;border:none" src="drvsim_scrub_09.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><img alt="drvsim_scrub_10" width="1664" height="877" style="margin:0;width:1664px;height:877px;border:none" src="drvsim_scrub_10.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">It is possible to observe that if Threshold_LS is reduced (red analysis), the scrub effect is also reduced on the front loaded wheel as soon as the value of 4% of longitudinal slip is exceeded. </p>
<p class="p_Normal">With the Smoothness_LS parameter, the user can tune the slope of the gain in the same way illustrated for the lateral margin.</p>
<p class="p_Normal">In general, the gain over longitudinal slip has a narrow-to-none operating window if the car model is including a restrictive TCS logic.</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><span style="font-weight: bold;">Gain Over Tire Loads</span></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">Tire Scrub Effect activation is also dependent on the normal load of the tires: this dependency has been included to tune the tool with every possible vehicle weight and weight distribution. The relative gain is computed using a forth power function over tire loads, considering that, in cornering maneuvers, the inner tires are less stressed, thus the scrub effect is lower. The user can set a value for the NF_M parameter, specifying the tire load (measured in Newton) threshold corresponding to a gain value of 1. The isolated effect of this parameter is explained by the following pictures.</p>
<p class="p_Normal">&nbsp;</p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Parameter Value</span></p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Analysis Colour</span></p>
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<td style="vertical-align:middle; width:433px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Baseline</span></p>
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<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">NF_M =10000[N]</p>
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<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">NF_M =8500[N]</p>
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<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Red</p>
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<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal" style="text-align: center;"><img alt="drvsim_scrub_11" width="359" height="318" style="margin:0px auto 0px auto;width:359px;height:318px;border:none" src="drvsim_scrub_11.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><img alt="drvsim_scrub_12" width="1664" height="877" style="margin:0;width:1664px;height:877px;border:none" src="drvsim_scrub_12.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><span style="font-weight: bold;">Mapping over Wheel Omega</span></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">This gain is meant to stretch the sinusoidal disturbance in its frequency. The user is able to adjust the mapping for the disturbance frequency with respect to rotational speed of the wheels. Values for ω_max parameter are inversely proportional to the frequency of the Tire Scrub Effect, as shown by the comparison of the following plots.</p>
<p class="p_Normal">&nbsp;</p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Parameter Value</span></p>
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<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Analysis Colour</span></p>
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<td style="vertical-align:middle; width:433px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Baseline</span></p>
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<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">ω_max=1</p>
</td>
<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Blue</p>
</td>
</tr>
<tr style="text-align:left;vertical-align:top;">
<td style="vertical-align:middle; width:433px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Mod</span></p>
</td>
<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">ω_max=2</p>
</td>
<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Red</p>
</td>
</tr>
</tbody>
</table>
</div>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal" style="text-align: center;"><img alt="drvsim_scrub_13" width="359" height="318" style="margin:0px auto 0px auto;width:359px;height:318px;border:none" src="drvsim_scrub_13.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><img alt="drvsim_scrub_14" width="1664" height="877" style="margin:0;width:1664px;height:877px;border:none" src="drvsim_scrub_14.png"/></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><span style="font-weight: bold;">Global Gain</span></p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">Finally, the user can adjust the global scaling of the tire scrub effect, directly proportional to the amplitude of the sinusoidal disturbance</p>
<p class="p_Normal">&nbsp;</p>
<div style="text-align: justify; text-indent: 0px; padding: 0px 0px 0px 0px; margin: 0px 0px 0px 23px;"><table style="border:none; border-spacing:0px; border-collapse:collapse;">
<thead>
<tr style="text-align:left;vertical-align:top;">
<th style="vertical-align:middle; width:433px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Case</span></p>
</th>
<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Parameter Value</span></p>
</th>
<th style="vertical-align:middle; width:700px; height:33px; background-color:#99ccff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;"><span style="font-size: 8pt; font-weight: bold;">Analysis Colour</span></p>
</th>
</tr>
</thead>
<tbody>
<tr style="text-align:left;vertical-align:top;">
<td style="vertical-align:middle; width:433px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Baseline</span></p>
</td>
<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">G=1.7</p>
</td>
<td style="vertical-align:middle; width:700px; height:33px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Blue</p>
</td>
</tr>
<tr style="text-align:left;vertical-align:top;">
<td style="vertical-align:middle; width:433px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: left; margin: 0px 0px 0px 23px;"><span style="font-weight: bold;">Mod</span></p>
</td>
<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">G=1.2</p>
</td>
<td style="vertical-align:middle; width:700px; height:35px; background-color:#ffffff; padding:0px; border:solid thin #000000;"><p style="text-align: center; margin: 0px 0px 0px 23px;">Red</p>
</td>
</tr>
</tbody>
</table>
</div>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal">&nbsp;</p>
<p class="p_Normal"><img alt="drvsim_scrub_15" width="1635" height="862" style="margin:0;width:1635px;height:862px;border:none" src="drvsim_scrub_15.png"/></p>

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